Theorems · Theorem · logic and foundations
Ordinal.opow_omega0
∀ {a : Ordinal.{u}}, 1 < a → a < Ordinal.omega0 → a ^ Ordinal.omega0 = Ordinal.omega0- Defined in
- Mathlib.SetTheory.Ordinal.Principal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LT.lt.leproof · cited by 2,189
- Ordinalstatement and proof · cited by 1,688
- le_of_ltproof · cited by 1,175
- LE.le.antisymmproof · cited by 507
- Ordinal.omega0statement and proof · cited by 197
- Order.one_le_iff_ne_zeroproof · cited by 32
- Ordinal.isSuccLimit_omega0proof · cited by 9
- Ordinal.opow_le_of_isSuccLimitproof · cited by 7
- Ordinal.right_le_opowproof · cited by 4
- Ordinal.isPrincipal_opow_omega0proof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- ONote.repr_opowproof · cited by 1
- Ordinal.natCast_opow_omega0proof · cited by 0